so hmmm  hmm which fraction is bigger, well, let's take a peek at their denominators, 3, 8, 2 and 4 ok....  now, let's multiply each fraction, by the other three denominators so, that is 2/3 we'll multiply it by 8*2*4 then 7/8 we'll multiply it by 3*2*4 and 1/2 by 3*2*4 and 3/4 by 3*8*2 so, what we'll end up with, is a denominator that is more or less a GCF, but the same for all $\bf \cfrac{2}{3}\cdot \cfrac{8\cdot 2\cdot 4}{8\cdot 2\cdot 4}\implies \cfrac{2}{3}\cdot \cfrac{64}{64}\implies \boxed{\cfrac{128}{192}} \\\\\\ \cfrac{7}{8}\cdot \cfrac{3\cdot 2\cdot 4}{3\cdot 2\cdot 4}\implies \cfrac{7}{8}\cdot \cfrac{24}{24}\implies \boxed{\cfrac{168}{192}} \\\\\\$ $\bf \cfrac{1}{2}\cdot \cfrac{3\cdot 8\cdot 4}{3\cdot 8\cdot 4}\implies \cfrac{1}{2}\cdot \cfrac{96}{96} \implies \boxed{\cfrac{96}{192}} \\\\\\ \cfrac{3}{4}\cdot \cfrac{3\cdot 8\cdot 2}{3\cdot 8\cdot 2}\implies \cfrac{3}{4}\cdot \cfrac{48}{48}\implies \boxed{\cfrac{144}{192}}$ now, which one is the largest? notice, all denominators are the same now